Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Multiple-Choice Question 2.1 (extended)
Students were asked the following clicker question (Classroom Performance System, einstruction.com) near the end of their learning cycle.
A ball is thrown and released such that it initially travels upwards. While it is momentarily at its highest point, its acceleration is __________. (Up = +y direction; neglect air resistance ("free fall").)
(A) +9.80 m/s^2.
(B) 0 m/s^2.
(C) –9.80 m/s^2.
(D) (More than one of the above choices.)
(E) (None of the above choices.)
(F) (I'm lost, and don't know how to answer this.)
Sections 70854, 70855
(A) : 1 student
(B) : 32 students
(C) : 7 students
(D) : 0 students
(E) : 0 students
(F) : 0 students
A separate, but related question was asked after displaying the tallied results shown above.
Which graph represents a ball thrown upwards, to falling back downwards? (Up = +y direction; neglect air resistance ("free fall"); t = 0 is immediately just after ball is released; axes are not to scale.)
Sections 70854, 70855
(A) : 7 students
(B) : 24 students
(C) : 2 students
(D) : 0 students
(E) : 0 students
(F) : 1 student
(G) : 5 students
(H) : 2 students
Correct answer: (B)
Whole-class discussion facilitated by the instructor goes over the types of free fall motion the other graphs (A), (C) and (D) represent, but the key to understanding graph (B) is that the upwards velocity decreases (becomes a smaller positive number) until it is momentarily zero at its highest position, and then this velocity increases downwards (becomes a larger negative number) as the ball falls back downwards.
The original question ("A ball is thrown and released such that it initially travels upwards") was asked again, with the following results.
Sections 70854, 70855
(A) : 0 students
(B) : 7 students
(C) : 34 students
(D) : 0 students
(E) : 0 students
(F) : 0 students
In this whole-class discussion, students realize that the slope of the v_y versus t graph gives the acceleration, which is always a constant negative value, even when the velocity is momentarily zero, and thus a_y = -9.8 m/s^2 is the acceleration throughout the trajectory of the ball.
A student asked when the speed of the ball "matters" (i.e., when does drag become important?). Not in free fall (zero air resistance) conditions, but it does matter under realistic conditions, especially with greater and greater speeds.
Pre- to post- peer-interaction gains:
pre-interaction correct = 18%
post-interaction correct = 83%
Hake, or normalized gain <g> = 79%
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